Steady-state analysis of a bistable system subject to a coloured multiplicative noise and a white additive noise with coloured cross-correlated noises

The steady-state properties of a bistable system are investigated when both the multiplicative noise and the coupling between additive and multiplicative noises are coloured with different values of noise correlation times tau(1) and tau(2). After introducing a dimensionless parameter R(R = alpha/D, D is the intensity of the multiplicative noise and a is the intensity of the additive noise), and performing the numerical computations, we find the following points: (1) For the case of R > 1, lambda (the intensity of correlation between additive and multiplicative noises), tau(1) and tau(2) can induce the stationary probability distribution (SPD) transition from bimodal to unimodal in structure, but for the cases of R = 1, the bimodal structure is preserved; (2) a can also induce the SPD transition from bimodal to unimodal in structure; (3) the bimodal structure of the SPD exhibits a symmetrical structure as D increases.